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Math Help - fractions problem

  1. #1
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    fractions problem

    When Tony was cleaning his refrigerator he found 2 bottles of mayo. Looking at the labels, he noticed that the capacity of the larger bottle was twice the capacity of the smaller bottle. He estimated that the smaller bottle was about \frac{1}{3} full of mayo and the larger bottle was about \frac{2}{3} full of mayo. He poured all the mayo from the smaller bottle into the larger bottle. Then, about how full was the larger bottle?
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  2. #2
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    Let c represent the capacity of the larger bottle. Then the capacity of the smaller bottle is (1/2)c. Since the larger bottle is 2/3 full, it contains (2/3)c mayo. The smaller bottle contains (1/3)(1/2)c = (1/6)c mayo. When you pour the smaller bottle into the larger one, you get (2/3)c + (1/6)c = (5/6)c mayo. Therefore, the larger bottle is 5/6 full of mayo.
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  3. #3
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by mjoshua View Post
    When Tony was cleaning his refrigerator he found 2 bottles of mayo. Looking at the labels, he noticed that the capacity of the larger bottle was twice the capacity of the smaller bottle. He estimated that the smaller bottle was about \frac{1}{3} full of mayo and the larger bottle was about \frac{2}{3} full of mayo. He poured all the mayo from the smaller bottle into the larger bottle. Then, about how full was the larger bottle?
    Let the capacity of small bottle be x.

    then the capacity of large bottle is y=2x.

    The small bottle has \frac{x}{3} volume of mayo.

    The larger bottle has \frac{2y}{3} bottle of mayo.

    So after pouring all the mayo from the smaller to the larger bottle, the amount of mayo in the larger bottle is:

     \frac{x}{3} +\frac{2y}{3}

    =  \frac{y}{6} +\frac{2y}{3} [since  y=2x,  x = \frac{y}{2} that gives   \frac{x}{3} =  \frac{y}{6} ]

    =  \frac{5y}{6}

    so the large jar should be  \frac{5}{6} full
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  4. #4
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    Ahh, there we go! Now that makes sense Thanks guys!
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